How can you append a material with nodes?
Be careful not to confuse material nodes with compositing nodes. The composition nodes are kind of like filters or effects in a video editor, and are applied after or during the render on the image, rather than on the mesh. Your material nodes are being appended just fine, but the compositing nodes are not being appended since they are not related to your light saber object, but rather to the blender scene being rendered.

To copy them, you can create a node group in your original blend file, and append the node group from your second file, or you can click and drag to select all the nodes in the original blend file's window, and ctrl+c copy them, and open your second blend file and ctrl+v paste them. For more info, read this question How do you import a Compositing Node Set-up?.